There's a rather loud buzzing noise coming from behind the dash on the drivers size of the GTX. It doesn't always happen, at first I thought it might have been the radiator fan but it's not and it can't be heard outside of the car only from inside. Any ideas?

Is it definitely the drivers side?
There is a recirculation motor that sits behind the dash but nearer the glovebox side - this has been known to make a racket when its opening the fresh air flap, some of them have ruined cogs where the flap has been jammed for years and its stripped the teeth off..!

When I bought my 2nd 406 ( ex-taxi, eBay purchase, many issues ) the fresh air flap had to be broken off as it was stuck solid, you can only imagine the smell in that car when I first got it....

Another possibility you get with 110's of that age is a buzzing noise from the bulkhead area that typically lasts for maybe 15-20 seconds after stopping the engine, (I think it comes from one the vacuum solenoids that control the egr/wastegate/air doser)

The noise stops as soon as you turn off the engine. It seems to come and go sometimes only on for a few minutes other times it lasts for 10 to 15 minutes. Strangely it can't be heard in the engine bay and after a bit more listening it seems to be coming more from the middle of the dash.

It will probably be a heater flap motor. The temperature one is pretty active most of the time, try changing the temperature when its doing it - or not doing it. If its not that could be another flap motor stacking.

It's easy to check the flap, pop out the pollen filter & whilst looking down the hole under the pollen filter aperture
Get a assistant to press the recirculate button you should see the flap open & close if all is well.
Obviously with the ignition on.

The recirculation flap motor is not operated for this long, at most ~ 10-20 seconds... Probably it's a temperature flap motor as PeterN suggests. Also because you hear it from the middle of the dash, that is where they are. There are two of these temperature flap motors: